For most people, Mathematics is frightening. Many people avoid learning Math. In fact, mathematics is closely related to our daily lives at home, school, and other public places. Learning mathematics has many advantages, including improving logical and reasoning skills, problem-solving abilities, and comprehension of how the world functions. So, how can children learn mathematics in an engaging and easy-to-understand manner?
Montessori Mathematics Program
Indirect Preparation
Before working with mathematics, Montessori children get indirect preparation in the areas of Practical Life, Sensory, and Language. In the Practical Life area, children practice concentration and learn a work cycle, which will be very useful later in their mathematics studies. In the Sensorial area, children have direct experience with the concepts of dimension and comparison through touch. In the Language area, children learn writing and reading skills, which help them grasp mathematical language and solve problems that require those skills. All of these activities indirectly train children to think and work mathematically.
Number 1-10
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Children learn the most basic concept: recognizing numbers 1-10. In Montessori education, quantities of 1-10 are introduced concretely by using Number Rod, followed by written symbols using Sandpaper Numbers. The Number Rods and Cards activity combines the concepts of quantity and symbol. The number 0 is presented subsequently through the Spindle Box, which allows children to physically experience an empty box while the other boxes are filled. Following that, children begin learning to count from 1 to 10 and practice the relationship between quantity and written symbols using Cards and Counters.
Overview of the Decimal System
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After children learn the numbers 1-10, decimal system is introduced. Golden Beads is the main material for teaching the decimal system, which begins with the name of the power of ten: units (unit beads), tens (ten bars), hundreds (hundred squares) and thousands (thousand cubes). Then, children will learn to count with the decimal system 1-9, 10-90, 100-900 and 1000. After that, children will learn to recognize quantities using golden beads through group games. After that, number cards are used to represent a written symbol. The series of introductions to the decimal system ends with the Bird’s Eye View activity as a combination of quantities and symbols.
Linear Counting
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The stages of linear counting still follow the concept of concrete to abstract by introducing quantity first, followed by written symbols. Following are the stages:
- Introduction to Short Bead Stairs
- Learning the names of quantities 11-19
- Learning the names of written symbol 11-19 with Séguin Board A
- Combining quantities & written symbols with Séguin Board A
- Learning the names of quantities 11-90
- Learning the names of written symbols with Séguin Board B
- Combining quantities & written symbols with Séguin Board B
- One Hundred Beads Chain.
Group Operations
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Group Operations are carried out in groups. Two children will work together to solve decimal system operations using Golden beads as concrete representations of quantities. Decimal System operations include addition, multiplication, subtraction, and division, both static and dynamic. Through this activity, children gain concrete and enjoyable experience by completing mathematical operations in group.
Introduction to Recording
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At this stage, children use various materials to record mathematical operations. The aim is to give children further experience with number combinations, number bonds, and recording exercises. In addition, children learn to develop speed in calculations, study tables, and memory and logic in Mathematics.
Individual Operation
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Children eventually begin individual operations training after gaining practical experience, working in groups, and recording exercises. At this stage, children use Stamp Game material using written symbols to solve mathematical operations and do recording individually.
Uniqueness of Montessori Mathematics
The Montessori Mathematics curriculum differs significantly from what most of us who have studied mathematics in traditional schooling have learned. The mathematics of Montessori is unique, systematic, and comprehensive.
Tactile Experience
Children can hold and touch all of the Mathematics items. Their tactile experience exhibits a strong sense of quantity. When the children pick a bead with their pincer grip, they can feel that the unit is small and light, representing the smallest quantity. When the children hold a thousand cube with their palms, they can feel that the cube is big and heavy, representing the largest quantity.
Decimal System
In traditional education, after children learn the numbers 1-10, they will learn the numbers 11, 12, 13 and so on. The way that the Montessori approach genuinely presents the decimal system after learning numbers 1 – 10 is completely different from the traditional approach. They learn units, tens, hundreds, and thousands and then count 1-9, 10-90, 100-900 and 1000. Does it seem strange? Why do young children need to learn to count to thousands? Can they? Yes, they can! This is actually easier than forcing children to memorize number 11, 12 and so on.
Concrete to Abstract
Mathematics is abstract; thus, in order for children to understand it, they must first experience abstract concepts in concrete form. The typical order of operations in Montessori mathematics is quantity (concrete), written symbols (abstract), and finally combining quantity and symbols.
Order of Mathematical Operations
What did you learn after you completed the addition operation? Most of us will instantly respond with subtraction. That is not how Montessori math works. Children in Montessori education learn multiplication after addition and division after subtraction since the principles are similar. Multiplication is repeated addition, while division is repeated subtraction.
Conclusion
It’s beautiful, isn’t it? Montessori exposes children to the huge and seemingly endless world of mathematics, cultivates appreciation and love, and then explores that world with great curiosity and excitement. There will be no memorizing, coercion, or promises of rewards. If you knew this all along, wouldn’t you want it too for you and now for your children?
FAQ
The Montessori math curriculum progresses from concrete to abstract concepts, allowing children’s understanding of math operations to develop gradually. Initially, children use manipulatives to physically add, subtract, multiply, and divide before advancing to memorizing math facts.
Children learn to organize numbers in their minds, comprehend the space objects occupy, and grasp the real-world significance of numbers. The Montessori math approach equips children with a deeper understanding of what numbers represent in the physical world, preparing them to use pen and paper effectively.
The Montessori math program focuses on three distinct concepts: number, quantity, and their relationship. Children use concrete materials to explore each concept individually. They are then taught to label a quantity with the corresponding numerical symbol.